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That's a very strange question. Can you find the source that shows different stroke orders? (YOU doesn't say where the images come from either). I've personally learned: 1st horizontal then vertical strokes. My old kanji book shows a same stroke order (horizontal first) and my 3 Chinese dictionaries show the same order as well for both characters.
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repecmpsJun 11 '11 at 7:27

Forget it, I find all online kanji dictionaries show a different stroke order. (that's different with Chinese characters, strange...)
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repecmpsJun 11 '11 at 7:45

3 Answers
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It has to do with the stroke order of the part underneath it. For this example, I'll refer to 左 as ナ and エ, and 右 as ナ and ロ. For 左、 since the first stroke of the underneath part (the エ） is horizontal, the ナ is started with the horizontal stroke. For 右, since the first stroke of the ロ is vertical, the ナ is also started vertically.

Similarly for 有 and 布. Since 月 and 巾 both start vertically, the ナ also starts vertically. Can't think of anymore off the top of my head where the ナ starts horizontally. But the rule is to look to the first stroke underneath the ナ.

I'm not quite sure I understand his post. I don't think he's wrong, but his doesn't really tell you which is supposed to be a longer stroker or a shorter stroke. Like I said, if you just look at the bottom part, you can figure it out for any arbitrary kanji of that form.
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istrasciJun 1 '11 at 2:50

This looks like a handy way to remember which order I should use for which character, and that I appreciate. But it doesn't answer why the order is different.
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Garrett AlbrightJun 11 '11 at 12:58

@Garrett - Then you looked way more into the meaning of the word "why" than I did.
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istrasciJun 12 '11 at 0:39

1

It would make more sense if you say that, if the lower part starts with a horizontal stroke as in 左, then the last stroke of the upper part should be vertical to minimize movement (doing vertical, then horizontal requires less movement than repeating horizontal strokes), which means the first stroke is horizontal. Similarly for the other case.
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user458Jul 7 '11 at 2:20

There is some meaning that shorter stroke mean 手のひら "Palm", longer one is 腕 "arm".

Normally, shorter stroke which mean "手のひら" write first most of the time, so according to original kanji, 右 "Right" need to write a vertical slant stroke first and 左 "Left" need to write horizonal stroke first.

Although the modern characters are very similar, they show a remarkable difference when written in seal script. Since the short stroke representing the hand is drawn first, and the hands are on the corresponding sides of the character, the stroke drawn from the character's meaning to the opposite (e.g. from left to right on 左) is drawn first.

(Yes, I admit it. I lifted this from Tomehane. It's a must read for those interested in calligraphy.)

In these pictures I see both horizontal lines being drawn first, then comes the vertical one.
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repecmpsJun 11 '11 at 7:34

The horizontal stroke in 右 is marked "2" in the picture. The hand is the slanted stroke.
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Ignacio Vazquez-AbramsJun 11 '11 at 7:39

hmm? The stroke marked 2 is the one going right down to the bottom in both characters. I call this vertical, although in 右 this stroke starts horizontally.
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repecmpsJun 11 '11 at 8:22

Do this. Raise your right arm and point it out forwards from you, with your right hand spread. Then bend your right elbow so that your forearm is aligned left-to-right in front of you. From the end of your pinky to the end of your thumb is stroke 1. From the tip of your middle finger to your elbow is stroke 2.
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Ignacio Vazquez-AbramsJun 11 '11 at 8:31

Would you post a link to the Tomehane book you mentioned?
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Nate GlennApr 16 '14 at 6:33